Given is the right triangle ABC with altitude CO . Which one of the following statements is true and contributes to the proof of the Pythagorean Theorem? (1 point) Responses △ABC∼△BOC triangle upper A upper B upper C congruent to triangle upper A upper C upper O △AOC∼△BOC triangle upper A upper B upper C congruent to triangle upper A upper C upper O △AOC∼△COB triangle upper A upper B upper C congruent to triangle upper A upper C upper O △ABC∼△AOC

Question

GPT-4o mini · Answer

To prove the Pythagorean Theorem using the properties of similar triangles in right triangle \( ABC \) with altitude \( CO \), the correct statement that contributes to the proof is:

△AOC∼△BOC

This statement indicates that triangle \( AOC \) is similar to triangle \( BOC \). This similarity arises from the fact that both triangles share angle \( C \) and each has a right angle, which establishes the angle-angle (AA) criterion for similarity.

Using this similarity, we can set up proportions based on the corresponding sides of the triangles, leading us to the relationship between the squares of the lengths of the sides, thereby proving the Pythagorean Theorem \( a^2 + b^2 = c^2 \).